Theorems · Theorem · group theory
Subgroup.relIndex_eq_one
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H.relIndex K = 1 ↔ K ≤ H- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Subgroup.relIndexstatement · cited by 72
- Subgroup.index_eq_oneproof · cited by 9
- Subgroup.subgroupOf_eq_topproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.card_eq_oneproof · cited by 4
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- IsPGroup.le_or_disjoint_of_coprimeproof · cited by 1
- Subgroup.commensurable_adjoinNegOne_selfproof · cited by 1
- Subgroup.normal_of_index_eq_minFac_cardproof · cited by 0
- Subgroup.index_strictAntiproof · cited by 0